Incremental Bayesian Learning

Use case

If the data is observed sequential, we can update our current predictions from the knowledge of the past predictions.

$$P\left(\mathbf{w}\mid D_{k+1}\right)=\frac{P\left(D_{k+1}\mid \mathbf{w}\right)P\left(\mathbf{w}\mid D_k\right)}{P\left(D_{k+1}\right)}$$

Where,

• $\text{w}\to$ Model Parametr to be learned.
• $D\to$ Data

Note: Here the posterior from the previous step becomes the prior for the current step.